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A114199 Row sums of a Pascal-Fibonacci triangle. 2
1, 2, 4, 8, 17, 38, 87, 200, 458, 1044, 2373, 5388, 12233, 27782, 63112, 143392, 325805, 740266, 1681935, 3821412, 8682310, 19726316, 44818473, 101828344, 231355953, 525645354, 1194276812, 2713420728, 6164945513, 14006877390 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
COMMENTS
Binomial transform of double Fibonacci sequence A103609(n+2). Row sums of A114197.
LINKS
Sergio Falcón, Binomial Transform of the Generalized k-Fibonacci Numbers, Communications in Mathematics and Applications (2019) Vol. 10, No. 3, 643-651.
FORMULA
G.f.: (1-x)^2/(1-4x+5x^2-2x^3-x^4);
a(n) = Sum_{k=0..n} Sum_{j=0..n-k} C(n-k, j)*C(k, j)*F(j);
a(n) = Sum_{k=0..n} C(n, k)*F(floor((k+2)/2)).
MATHEMATICA
LinearRecurrence[{4, -5, 2, 1}, {1, 2, 4, 8}, 30] (* Harvey P. Dale, Dec 07 2015 *)
CROSSREFS
Sequence in context: A084635 A294529 A154222 * A006196 A089796 A112482
KEYWORD
easy,nonn
AUTHOR
Paul Barry, Nov 16 2005
STATUS
approved

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Last modified March 29 00:26 EDT 2024. Contains 371264 sequences. (Running on oeis4.)